Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral

Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral

碩士 === 國立中正大學 === 數學系應用數學研究所 === 105 === This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove tha...

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Main Authors: LUO, YI-XUAN, 羅易宣
Other Authors: CHO, CHIEN-HONG
Format: Others
Language:en_US
Published: 2017
Online Access:http://ndltd.ncl.edu.tw/handle/383xuy
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spelling ndltd-TW-105CCU005070072019-05-15T23:24:28Z http://ndltd.ncl.edu.tw/handle/383xuy Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral LUO, YI-XUAN 羅易宣 碩士 國立中正大學 數學系應用數學研究所 105 This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove that our numerical solutions converge to the exact solution and that the numerical blow-up time also converges to the exact blow-up time. Several numerical examples concerning the blow-up behavior of odd p and the special case p=2 are also reported. CHO, CHIEN-HONG 卓建宏 2017 學位論文 ; thesis 27 en_US
collection NDLTD
language en_US
format Others
sources NDLTD
description 碩士 === 國立中正大學 === 數學系應用數學研究所 === 105 === This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove that our numerical solutions converge to the exact solution and that the numerical blow-up time also converges to the exact blow-up time. Several numerical examples concerning the blow-up behavior of odd p and the special case p=2 are also reported.
author2 CHO, CHIEN-HONG
author_facet CHO, CHIEN-HONG
LUO, YI-XUAN
羅易宣
author LUO, YI-XUAN
羅易宣
spellingShingle LUO, YI-XUAN
羅易宣
Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
author_sort LUO, YI-XUAN
title Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
title_short Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
title_full Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
title_fullStr Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
title_full_unstemmed Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
title_sort numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
publishDate 2017
url http://ndltd.ncl.edu.tw/handle/383xuy
work_keys_str_mv AT luoyixuan numericalapproximationfortheblowupsolutionsofapartialdifferentialequationwithconservedfirstintegral
AT luóyìxuān numericalapproximationfortheblowupsolutionsofapartialdifferentialequationwithconservedfirstintegral
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